Let y = y(x) be a solution curve of the differential equation (1… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 11 April, Shift 1Separation of Variables

Let $y = y(x)$ be a solution curve of the differential equation $(1 - x^2 y^2) \, dx = y \, dx + x \, dy$ If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$ , then a value of $\alpha$ is:

A
$\frac{1 + 3e^2}{2(3e^{2} - 1)}$
B
$\frac{1 - 3e^2}{2(3e^{2} + 1)}$
C
$\frac{3e^2}{2(3e^{2} - 1)}$
D
$\frac{3e^2}{2(3e^{2} + 1)}$

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